Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 2. SV-P wave propagation

Abstract

Part I of these two related papers considered the analytical evaluation of singular integrals for anti-plane boundary elements, the results of which were then applied to the evaluation of scattering problems involving SH waves. This second part provides an extension of these results to the more complicated case of in-plane boundary elements, and presents their application to scattering problems involving SV-P waves. First, the singular integrals for constant, linear and quadratic boundary elements are evaluated a in closed form. Thereafter, the formulation is used to model cylindrical inclusions in a two-dimensional elastic medium illuminated by dynamic in-plane (plane-strain) line sources. The boundary element method (BEM) results are then compared with the known analytical solutions for these problems.